The emergence of the compression standards JPEG, MPEG, H.26x has enabled many consumer and business multimedia applications, where the multimedia content is disseminated in its compressed form. However, many applications require processing of the multimedia content prior to presentation. A very frequent process is that of down-sampling (down-scaling, down-sizing) the compressed image.
Thus, in applications, such as image and video browsing, it may be sufficient to deliver a lower resolution image or video to the user. Based on user's input, the media server could then provide the higher resolution image or video sequence.
Also, composting several MPEG video sources into a single displayed stream is important for MPEG video applications as for example advanced multimedia terminals, interactive network video and multi-point video conferencing. Composting video directly in the compressed domain reduces computational complexity by processing less data and avoiding the conversion process back and forth between the compressed and the uncompressed data formats. In compression standards (MPEG, H.26x), compression is computationally 3 to 4 times more expensive than decompression. Compressed domain based down-sampling can be used to implement an efficient picture-in-picture system for MPEG compressed video and can result in significant savings.
Furthermore, efficient transcoding should be able to cope with different quality of services in the case of multi-point communications over POTS, ISDN, and ADSL lines. A HDTV down conversion decoder can decode the Grand Alliance HDTV bitstreams and display them on SDTV or NTSC monitors.
Conventional techniques for down-scaling rely on decompressing the bitstreams first and then applying the desired processing function (re-compression).
The down-sampling of a still image in the spatial domain consists of two steps. First the image is filtered by an anti-aliasing low pass filter and then it is sub-sampled by a desired factor in each dimension. For a DCT-compressed image, the above method implies that the compressed and quantised image has to be recovered first into the spatial domain by inverse DCT (IDCT or DCT−1) and then undergo the procedure of filtering and down-sampling as illustrated in FIG. 1a. 
A direct approach would be to work in the compressed domain, where both operations of filtering and down-sampling are combined in the DCT domain. This could be done by cutting off DCT coefficients of high frequencies and using the IDCT with a smaller number of coefficients to reconstruct the reduced resolution image. For example, one could use the 4×4 coefficients out of the 8×8 and perform the IDCT on these coefficients in order to reduce the resolution by a factor of 2 in each dimension as illustrated in FIG. 1b. This technique does not result in significant compression gains and requires encoders and decoders to be able to handle 4×4 DCTs and IDCTS. It also requires run-length coding schemes to be optimised for the 4×4 case. Furthermore, this method results in significant amount of blocking effects and distortions, due to the poor approximations introduced by simply discarding higher order coefficients.
This technique would be more useful if 16×16 DCT blocks was used and were 8×8 DCT coefficients were kept in order to obtain the down-sampled. However, most image and video compression standards, like JPEG, H.26x, and MPEG, segment the images into rectangular blocks of size 8×8 pixels and apply the DCT on these blocks. Therefore, only 8×8 DCTs are available. One way to compute the 16×16 DCT coefficients is to apply inverse DCT in each of the 8×8 blocks and reconstruct the image.
Then the DCT in blocks of size 16×16 could be applied and the 8×8 out of the 16×16 DCTs coefficients of each block could be kept. This would lead to a complete decoding (performing 8×8 IDCTS) and re-transforming by 16×16 DCTs, something that would require 16×16 DCT hardware or software.
However, if one could compute the 8×8 out of the 16×16 DCT coefficients by using only 8×8 transformations, then this method would be faster and it would perform better than the one that uses the 4×4 out of the 8×8. This would also mean that by avoiding the computation of DCTs of size 16×16, the memory requirements could also be reduced as illustrated in FIG. 1c. 
Furthermore, in the international patent application PCT/SE98/00448 a method and a device for encoding/decoding DCT compressed images in the frequency domain are described, and which application is hereby is enclosed herein by reference.